The Annals of Statistics

Semiparametrically point-optimal hybrid rank tests for unit roots

Bo Zhou, Ramon van den Akker, and Bas J. M. Werker

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Abstract

We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are based on the ranks of the increments of the observations, their average and an assumed reference density for the innovations. The tests are semiparametric in the sense that they are valid, that is, have the correct (asymptotic) size, irrespective of the true innovation density. For a correctly specified reference density, our test is point-optimal and nearly efficient. For arbitrary reference densities, we establish a Chernoff–Savage-type result, that is, our test performs as well as commonly used tests under Gaussian innovations but has improved power under other, for example, fat-tailed or skewed, innovation distributions. To avoid nonparametric estimation, we propose a simplified version of our test that exhibits the same asymptotic properties, except for the Chernoff–Savage result that we are only able to demonstrate by means of simulations.

Article information

Source
Ann. Statist., Volume 47, Number 5 (2019), 2601-2638.

Dates
Received: March 2017
Revised: June 2018
First available in Project Euclid: 3 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.aos/1564797858

Digital Object Identifier
doi:10.1214/18-AOS1758

Mathematical Reviews number (MathSciNet)
MR3988767

Subjects
Primary: 62G10: Hypothesis testing 62G20: Asymptotic properties
Secondary: 62P20: Applications to economics [See also 91Bxx] 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Unit root test semiparametric power envelope limit experiment LABF maximal invariant rank statistic

Citation

Zhou, Bo; van den Akker, Ramon; Werker, Bas J. M. Semiparametrically point-optimal hybrid rank tests for unit roots. Ann. Statist. 47 (2019), no. 5, 2601--2638. doi:10.1214/18-AOS1758. https://projecteuclid.org/euclid.aos/1564797858


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Supplemental materials

  • Supplement to “Semiparametrically optimal hybrid rank tests for unit roots”. This supplemental file contains technical proofs for propositions and theorems in the main context.